My iPhone 4 is constantly low on memory when downloading large Apps from the App Store.
I always get a message saying remove photos and videos to get space for new App.
I have been to Apple to sort out problem but did not work. The video are very important with sensitive info. How do I move these videos to my hard drive?

I like Image Capture and PhoneView for getting files off (and back on in PhoneView's case) the iPhone. A lot of what I snap are screen capture and I'd rather just have a folder to dump the media so I can sort and archive it as needed.

iPhoto doesn't necessarily open when you connect your iPhone unless you have specifically set it to do this.
You didn't mention if you were using a Windows or a Mac.
If you do use a Mac, then image capture will do the trick. Head on into ur Applications folder and fire up image capture, and with the phone connected via usb you can see and import everything including pics and videos.